Emotion analysis of on-line user generated textual content is important for natural language processing and social media analytics tasks. Most of previous emotion analysis approaches focus on identifying users’ emotional states from text by classifying emotions into one of the finite categories, e.g. joy, surprise, anger and fear. However, there exists ambiguity characteristic for the emotion analysis, since a single sentence can evoke multiple emotions with different intensities. To address this problem, we introduce emotion distribution learning and propose a multi-task convolutional neural network for text emotion analysis. The end-to-end framework optimizes the distribution prediction and classification tasks simultaneously, which is able to learn robust representations for the distribution dataset with annotations of different voters. While most work adopt the majority voting scheme for the ground truth labeling, we also propose a lexicon-based strategy to generate distributions from a single label, which provides prior information for the emotion classification. Experiments conducted on five public text datasets (i.e., SemEval, Fairy Tales, ISEAR, TEC, CBET) demonstrate that our proposed method performs favorably against the state-of-the-art approaches.